Slow waves of neuronal activity are a fundamental component of sleep that are proposed to have homeostatic and restorative functions. Despite this, their interaction with pathology is unclear and there is only indirect evidence of their presence during wakefulness. Using intracortical recordings from the temporal lobe of 25 patients with epilepsy, we demonstrate the existence of local wake slow waves (LoWS) with key features of sleep slow waves, including a down-state of neuronal firing. Consistent with a reduction in neuronal activity, LoWS were associated with slowed cognitive processing. However, we also found that LoWS showed signatures of a homeostatic relationship with interictal epileptiform discharges (IEDs): exhibiting progressive adaptation during the build-up of network excitability before an IED and reducing the impact of subsequent IEDs on network excitability. We therefore propose an epilepsy homeostasis hypothesis: that slow waves in epilepsy reduce aberrant activity at the price of transient cognitive impairment.